On stochastic ordering and control charts for traffic intensity. Issue 4 (1st October 2016)

• Record Type: Journal Article
• Authors: Morais, Manuel Cabral; Pacheco, António
• Is Part Of: Sequential analysis. Volume 35:Issue 4(2016)
• Page Start: 536
• Page End: 559
• Publication Date: 2016-10-01
• Subjects: Control charts -- queueing systems -- run length -- stochastic ordering; 60E15 -- 62P30; Sequential analysis -- Periodicals; 519.54
• DOI: 10.1080/07474946.2016.1238266
• Languages: English
• ISSNs: 0747-4946

Abstract

ABSTRACT: Traffic intensity ( ρ ) is a crucial parameter of a queueing system because it is a measure of the average occupancy of a server. Expectedly, an increase in ρ must be detected quickly so that appropriate corrective actions are taken. In this article, we briefly review existing procedures used to monitor the traffic intensity of GI ∕ M ∕1, M ∕ G ∕1, and a few other queues. We focus on control charts to detect increases in ρ whose control statistics are integer-valued and/or can be (approximately) modeled by discrete time Markov chains. Finally, we investigate the stochastic monotonicity properties of the associated probability transition matrices and explore the implications of these properties to provide insights on the performance of such control charts.